IE 423 - PROJECT PART 3 - MUSTAFA & BENGİSU & FETHİ

Question 3.1.1.

Question 3.1.2.

Question 3.1.3.

The original image and the modified image are displayed side by side. In the modified image, pixels that fell outside the 0.001 probability limits of the assumed normal distribution have been changed to black. The calculated bounds for these limits are approximately 93.46 for the lower bound and 254.99 for the upper bound.

Observations:

The original image looks to be fairly light in color overall, which is consistent with the mean pixel value being on the higher side (174.22). In the modified image, we can see that only a few pixels have been turned black, suggesting that there were not many pixels with values below the lower bound or above the upper bound. This means there were few extreme values in the pixel data. The fact that there are few black pixels in the modified image indicates that the bulk of the pixel values were within the middle 99.8% of the assumed normal distribution.

Findings:

The majority of the pixel values are concentrated around the mean, which is typical for a distribution that has light tails, as indicated by the kurtosis value close to zero. The outliers that were changed to black are not visibly prominent in the modified image, which could mean that these outlier pixels were scattered and not clustered in any particular region of the image. This approach of modifying outlier pixels could be a rudimentary method for noise reduction in image processing if the assumption of normal distribution holds for the particular application. However, caution should be taken since, in this case, the normal distribution was not a perfect fit for the pixel value distribution. By changing outlier pixel values to black, we've essentially applied a very simple form of thresholding. This could be useful in image processing tasks where identifying or removing outliers is necessary, but more sophisticated methods would typically be used in practice to avoid assuming a normal distribution where it may not apply.

Question 3.1.4.

The original image is shown alongside the modified image where outlier pixels in each 51x51 patch have been turned black.

Observations:

The modified image with patches processed reveals a more pronounced pattern of black pixels compared to the earlier whole-image processing. This suggests that the local variances within each patch were taken into account, leading to the identification of different outliers than when considering the global distribution. The pattern of black pixels in the modified image does not appear to be random but seems to be somewhat regularly distributed across the image, which could indicate that the outliers are related to specific features or textures within the local patches. Findings:

This localized approach can be more sensitive to the nuances within small areas of an image, which is particularly useful in tasks such as texture analysis, anomaly detection, or image segmentation. By applying the thresholding operation on a per-patch basis, we've effectively adapted to local variations in pixel intensity, which might be more reflective of the actual content and structure within the image. The resulting black pixels in each patch show where the extreme values lie relative to the local statistics of that patch, not the global statistics of the entire image. This method, while more computationally intensive, can provide a more detailed analysis and potentially better results for certain applications where local context is crucial. However, it also may highlight the importance of choosing the right window size for analysis, as different sizes could significantly affect the identification of outliers.

In the modified image where the global distribution was used to identify outliers, 323 pixels were turned black.

In the modified image where each 51x51 patch was processed individually, 286 pixels were turned black.

It is interesting to note that the number of black pixels is slightly higher when considering the image as a whole compared to processing it in patches. This might be due to the fact that local variations within patches can sometimes mask the presence of outliers when using a global threshold, whereas a localized approach adjusts the threshold based on the specific distribution of each patch, potentially resulting in fewer outliers relative to the local context.